1. Field of the Invention
The present invention generally relates to deflectors, optical scanning units, and image forming apparatuses, and more specifically, to a deflector using a vibrating mirror, an optical scanning unit using the deflector, and an image forming apparatus.
2. Description of the Related Art
In conventional optical scanning units, polygon mirrors or galvanometer mirrors are used to deflect beams for writing images. In order to achieve high-resolution high-speed printing operations, the rotational speed of these mirrors has to be increased. However, there is a ceiling to increasing the rotational speed of the mirror because of various reasons, such as limitation in durability of the bearings, heat generation due to air resistance, and noise.
On the other hand, optical deflectors making use of micromachining of silicon have been researched and studied. A technique for monolithically and integrally fabricating a vibrating mirror (movable mirror), together with a torsion bar supporting the mirror on its axis, from a silicon substrate, has been suggested.
In this type, namely the integrally fabricated vibrating mirror with the torsion bar, the size of the mirror surface is small. Hence, one of the advantages of this type is that the reciprocating motion of the mirror is produced by resonance, and that high-speed operation is achieved. In addition, noise and power consumption are reduced because less driving force is required to swing the vibrating mirror.
However, in order to secure an angle of view equivalent to the polygon mirror, it is necessary to form a rotational torque in a wider scan angle range.
To solve this problem, for example, Japanese Laid-Open Patent Application Publication No. 2005-24721 describes a deflection mirror whereby a rotational torque is generated in the vicinity of a rotational axis.
More specifically, the deflection mirror described in Japanese Laid-Open Patent Application Publication No. 2005-24721 has a movable mirror which deflects a light beam; a torsion beam connected to the movable mirror and that defines the center of turning; and mirror oscillation means which generates torque to oscillate the movable mirror. The mirror oscillation means is provided adjacent to the movable mirror in the direction of the turning axis, and the torque is generated on the part at which r′<=A/4 is satisfied, where r′ stands for the distance between the movable mirror and the center of turning and A stands for the width (both wings) of the movable mirror.
In order to apply the deflector to an optical scanning unit having plural image forming stations and corresponding to a tandem type where a color image is formed by superposing the plural color images, as discussed in Japanese Laid-Open Patent Application Publication No. 2003-98459, it is necessary to provide plural vibrating mirrors and drive these mirrors at a common scanning frequency. However, the common scanning frequencies may not always coincide because of the moment of inertia of the vibrating units and the spring constant of the twisting members, which tend to vary due to the fluctuations in dimensions caused during the manufacturing process.
In response to this problem, for example, Japanese Laid-Open Patent Application Publication No. 2004-40355 describes a technique where mass load parts are provided at both ends of a mirror. In addition, Japanese Laid-Open Patent Application Publication No. 2002-228965 describes a technique where a torsion beam and a mirror part are simultaneously processed so as to achieve the resonance frequency.
As discussed above, by using the vibrating mirror instead of the polygon mirror, noise and power consumption can be reduced so that it is possible to provide an image forming apparatus suitable for an office environment.
Especially, in the optical scanning unit corresponding to the “tandem type”, a temperature distribution is generated in the housing receiving the optical scanning unit due to heat from the polygon mirror and the position of a reflection mirror or a scanning lens of an image formation optical system may be changed due to thermal strain. This may cause color drift or color change. If the increase of the temperature is prevented in the case of using a vibrating mirror, it is possible to form an image with high quality.
However, in the case of the vibrating mirror compared to the polygon mirror, first, there is a disadvantage in that the mirror surface is small.
Second, in this case, the scan angle is small. In order words, as the scanning frequency increases in accordance with scanning speed enhancement, the scan angle may be unable to catch up with the speed. Another limit is that the amount of the rotation angle per unit time drastically decreases in accordance with sinusoidal vibration as the scan angle nears its peak.
For this reason, only about half the entire scan angle can be effectively used when trying to achieve even dot intervals on the scanned surface.
Moreover, it is preferable to have a smaller image formation spot diameter to bring the shape of the latent image potential distribution closer to rectangular and thus improve the resolution and maintain the evenness of the dot diameters. However, a Gaussian beam, in general, has the image formation property that ω0/ω is proportionate to the focal distance f of the image formation lens, where the diameter of the beam incident on the image formation lens is represented as ω0 and the diameter of the image formation spot is represented as ω.
This means that, when the angle of view becomes small with an insufficient scan angle, the focal distance f of the image formation lens inevitably becomes greater. To shrink the spot, the diameter of the beam ω0 needs to be increased, which means the mirror surface needs to be increased. For this reason, the situation is becoming more difficult to ensure a sufficient scan angle.
FIG. 1 is a view of the plate-shaped movable mirror and a graph.
A movable mirror shaped like a simple plate as shown in FIG. 1 will be considered.
The dimensions of the movable mirror are determined as 2r in width in a direction orthogonal to the rotational axis, d in width in a direction parallel to the rotational axis, and t in thickness. The dimensions of each twisting member are determined as h in length, and a in width. When the density of Si is ρ, and the material constant is G, the moment of inertia I=(4ρrdt/3)·r^2, and the spring constant K=(G/2h)·{at(a^2+t^2)/12}. Thus, the resonance frequency f0 is:f0=(½π)·√{square root over ( )}(K/I)=(½π)·√{square root over ( )}{Gat(a^2+t^2)/24LI}
The length of the torsion member h is almost proportional to the scan angle θ, and thus the scan angle θ can be expressed by:θ=κ/I·f0^2,where κ is a constant.  (1)
This means that the scan angle θ is inversely proportional to the moment of inertia I, and to increase the resonance frequency f0, the moment of inertia I must be reduced, or otherwise the scan angle θ would decrease. In other words, if 2r, the width in a direction orthogonal to the rotational axis, is simply increased, the scan angle θ would decrease in inverse proportion to the cube of the magnification factor.
On the other hand, the relationship between the torque T and the scan angle θ can be expressed by:θ=κ′·T/K where κ′ is a constant.  (2)
This means that, in order to secure the scan angle θ even if 2r, the width in a direction orthogonal to the rotational axis, is increased, it is necessary to generate the torque T proportion to the cube of the magnification factor.
In other words, since the rotational torque corresponding to a mirror surface size is generated and, as discussed above, the common frequency varies if plural vibrating mirrors are mixed, a method for securing the scan angle θ even if these are oscillated by a common scanning frequency fd is desirable.